Interaction of laser pulses with
atoms and molecules and
spectroscopic applications
Raman scattering
Pump
Vibrational levels
1
2
Pump
Stokes
1
3
anti-Stokes
Raman frequencies in spectrum due to modulation
of scattered light by molecular vibrations

P  ( q ) E , dI 
P
'    0
1
2
Inelastic scattering
2
[(
d
P
/
dt
)
n
]
3
4 c
dI ( ' )  I0 N d( ' )
d( ' )  '
4
 q
2
d
2
Electronic-resonance Raman scattering
 L   i , where i is resonance frequency
of electronic transition
Is  
i
1
i   L 2  i 2
Is  absorption coefficient
Characteristic Raman shifts for different bonds
A. Fadini and F.-M.Schnepel, Vibrational spectroscopy (Wiley, New York, 1989).
Impulsive excitation of low-frequency modes and pump-probe
study of oscillations of molecules and n-particles
Spectral component (normalized)
-1
=28cm
1.0
-1
=72cm
0.8
0.6
=20fs
0.4
0.2
=100fs
=50fs
50
100
0.0
0
150
-1
Frequency (cm )
200
Schematic of femtosecond spectroscopy in
a pump –probe configuration
Sample
Pump
Detector
The same principle is applicable
for n-particles and molecules
Probe
Femtosecond pump-probe spectroscopy of n-particles (d~15 nm)
Spectrum
Temporal response
8
Delay
0.25
7
0.20
N-particle
breathing mode
oscillations
Amplitude, a.u.
Amplitude, a.u.
6
5
4
3
2
0.15
0.10
0.05
1
0
0
10
20
30
40
Delay time, picosec
50
60
0.00
0
250
500
Frequency, GHz
750
1000
Schematic of the energy levels and
optical transitions in CARS
1
1
2
 ,  waves are all sent
1
2
3
Example: wave interaction in CARS,
Phase matching conditions
Requirement of phase matching
condition k3=k1+k1’-k2; three waves
create polarization wave (w3,k3)
Coherent anti-Stokes Raman spectroscopy (CARS)
Plane waves signal
 - nonlinear susceptibility tensor
sin(kL/ 2)
I CARS ~ CARS I I L
kL/ 2
d
1
where CARS ~
1 2 i
d 
2
2
2
1 2
2
But the CARS signal is limited by
limitations on the intensity!!!
The object can be destroyed.
k1 vector
k 2 mismatch
k  - 2wave
2

a
For gaussian beams L~
2
confocal parameter
2  2 d 

PCARS   P1 P2  

d
2
2
Physical values and processes for
strong-field laser physics
Intensity required for ionization (Ar)
𝐼 ≈ 1014
𝑊
𝑐𝑚2
Corresponding field strength
𝐸 = 1.9
× 108
𝑉
𝑐𝑚
atomic field strength (Hydrogen atom)
𝐸𝐻 = 6.1
× 109
𝑉
𝑐𝑚
New phenomena: ionization, high
harmonic generation (HHG),
fragmentation of molecules.
Typical atomic time-scale:
Bohr orbit time
2𝜋𝑎
𝜏=
= 152 𝑎𝑡𝑡𝑜𝑠𝑒𝑐𝑜𝑛𝑑𝑠
𝑐
Typical displacement of an ionized
electron in the laser field
𝑒𝐸
𝑥0 =
= 2.7𝑛𝑚
𝑚𝜔 2
Example: bandwidth requirement for
an attosecond pulse:
𝜏[𝐹𝑊𝐻𝑀] = 50𝑎𝑠
𝜏 × 𝛥𝑓 ≥ 0.44
𝛥𝑓 = 0.44 50 𝑎𝑠 =−> 𝜆 ≈ 30𝑛𝑚
ℎ𝜈[800𝑛𝑚] = 1.55𝑒𝑉
Ionization: Multiphoton and tunnel MECHANISMS
Leonid Keldysh, 1964: adiabaticity parameter
𝛾=
𝐼𝑝
2𝑈𝑝
𝛾 2 >> 1, multiphoton ionization,
probability 𝑃 ∝ 𝐸 2𝐾 , 𝐾 = 𝐼𝑛𝑡. 𝑃𝑎𝑟𝑡[𝐼𝑝 𝜔 + 1
2
2
2𝐸
𝑖
𝛾 2 << 1, tunnel ionization, probability 𝑃 ∝ exp −
3𝐹
Atomic system of units 𝑐 = 𝑚𝑒 = ℏ = 1
L V Keldysh, Soviet. Physics – JETP, 20(5), 1307 (1964) [Cited ≥3341 times!]
3
Multiphoton Ionization
(C)
Photoelectric effect
Multiphoton Ionization
𝑛 photons ionize an atom:
𝑛ℏ𝜔 + 𝐴 → 𝑒 − + 𝐴+
Multiphoton condition
(from Keldysh theory):
𝛾≫1
Above Threshold Ionization (ATI)
Kinetic energy of the electron:
𝐾𝐸 = 𝑛ℏ𝜔 − 𝑉𝐼𝐸
Ionization probability from
perturbation theory:
𝑃 𝐼 ∝ 𝐼𝑛
Courtesy of Nathan Hart and Gamze Kaya
Ionization of Argon by femtosecond pulses
𝐴𝑟 +
𝐴𝐷𝐾
𝐴𝑟 +
𝐴𝑟 2+
𝐴𝑟 3+
𝑃𝑃𝑇
Ionization of Ar, 200 fs pulses from a Ti:sapphire laser (800 nm).
The theoretical ion yields are, from left to right, calculated
from Szoke’s model (Perry et al 1988),
Perelomov, Popov, Terent’ev, 1966 (PPT) model,
Ammosov, Delone Kraynov, 1986 (ADK) theory and
strong-field approximation (SFA, Reiss, 1980).
S F J Larochelle, A Talebpoury and S L Chin,
J. Phys. B: At. Mol. Opt. Phys. 31, 1215 (1998)
Multiple ionization of Ar at higher peak intensities of 200 fs
pulses from a Ti:sapphire laser (800 nm).
S Larochelle, A Talebpoury and S L Chin,
J. Phys. B: At. Mol. Opt. Phys. 31 1201 (1998)
Dynamics of Ar ionization
by femtosecond pulses
Ar
Calculated ionization levels in argon for
a 19 fs laser pulse at a peak laser
intensity of 2.5 1015 𝑊/𝑐𝑚2 , using ADK
rates:
laser pulse envelope (black);
Ar(blue); 𝐴𝑟 + (green); 𝐴𝑟 2+ (red); 𝐴𝑟 3+
(pink); 𝐴𝑟 4+ (brown).
The right axis shows the predicted HHG
cutoff energy for the chosen laser
intensity, calculated from the cutoff rule
(Ecutoff=Ip+ 3:2Up).
Arpin et al. PRL 103, 143901 (2009)
Electron trajectories after
ionization
Cut off for high harmonic generation (HHG)
Cut off energy for HHG
𝐸𝑐𝑢𝑡 𝑜𝑓𝑓 = 𝐼𝑝 + 3.17𝑈𝑝
𝑚 𝑒𝐸
𝑈𝑝 𝑒𝑉 =
2 𝜔
2
= 9.33 ×
10−14 𝐼
𝑊
𝑐𝑚2
𝜆 𝜇𝑚
2
ℎ𝜈[800𝑛𝑚] = 1.55𝑒𝑉
𝑁𝐻𝐻𝑐𝑢𝑡 𝑜𝑓𝑓 [𝐴𝑟, 1014 𝑊 𝑐 𝑚2 ]
= (15.6𝑒𝑉 + 9.33𝑒𝑉 ) 1.55 𝑒𝑉 ≈ 17
𝑁𝐻𝐻𝑐𝑢𝑡 𝑜𝑓𝑓 [𝐴𝑟, 1015 𝑊 𝑐 𝑚2 ]
= (15.6𝑒𝑉 + 10 × 9.33𝑒𝑉 ) 1.55 𝑒𝑉 ≈ 71
Energy of electron returning parent atom
HHG in Argon (𝐼𝑝 =15.6 eV)
Intensity arb. unit
80
60
(b)
21th
40
13thth
13
23d cutoff
21st
19thth 17th th
19
17
th
11th
11
15th th
15
20
0
40
50
60
70
Wavelength nm
80
• Cutoff energy is at 23rd harmonic, 𝐸𝑐𝑢𝑡𝑜𝑓𝑓 = 35.6eV (34.8 nm)
• The laser power at 800 nm is 930 mW and a pulse duration 50 fs.
Three step model
Step 3
Step 2
Step 1
XUV
Tunnel ionization
Recombination
Electron acceleration in laser field
P. B. Corkum “Plasma perspective on strong field multi-photon ionization”
P. B. Corkum, F. Krausz, “Attosecond Science”
S. Haessler et. al., “Attosecond imaging of molecular electronic wavepackets”
Courtesy Muhammed Sayrac
Experiments on H2+ in intense laser fields (simplest molecule)
• Photodissociation: H2+ + nhν
• Coulomb explosion: H2+ + nhν
(>1012
W/cm2)
H+ + H
H+ + H+ + e-
At intensities
the coupling between 1sσg and
2pσu becomes very strong
(Pavicic, 2005)